"that the first square of the far right column should be light-coloured, endorsed by Pedro Damiano in the end of the 15th century. More recently, some varieties have employed three-dimensional boards, in which the third dimension is usually another two-dimensional board. The Raumschach variant utilises five boards of twenty-five squares each, totalising 125 squares. Another noteworthy variant, ""Star Trek"" Chess, utilises a board of sixty-four squares divided into seven levels. In 2003, the ex-world champion Garry Kasparov faced the chess engine X3D Fritz in a series of four matches in a virtual environment, where the computer-generated board hovered in the"
"rules were most recently revised in 2017. Chess is played on a square board of eight rows (called ' and denoted with numbers ""1"" to ""8"") and eight columns (called ' and denoted with letters ""a"" to ""h""). The colors of the 64 squares alternate and are referred to as ""light"" and ""dark"" squares. The chessboard is placed with a light square at the right-hand end of the rank nearest to each player. By convention, the game pieces are divided into white and black sets, and the players are referred to as ""White"" and ""Black"" respectively. Each player begins the"
"play on a board ruled into a grid of 15 ""ranks"" (rows) and 15 ""files"" (columns) with a total of 225 squares. The squares are undifferentiated by marking or color, unlike a Western chess board. Each player has a set of 65 pieces of 29 different types. In all, a player must remember 36 different moves. Each piece has its name written on it in Japanese kanji. The writing is typically in black. On the reverse side of most pieces there are characters to indicate the piece's promoted rank, typically written in red. The pieces are wedge-shaped and their orientation"
"Checkerboard A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which draughts (checkers) is played. Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, often black and white. An 8×8 checkerboard is used to play many other games, including chess, whereby it is known as a chessboard. Other rectangular square-tiled boards are also often called checkerboards. Given a matrix with formula_1 rows and formula_2 columns, a function formula_3, formula_4 returns true if the cell is white and false if the cell is black. The element formula_5"
"thus capturing that piece; and optionally of promoting the moving piece, if the move enters the ""promotion zone"", or if it is a capture and any part of it is in the promotion zone. Two players, Black and White (or 先手 ""sente"" and 後手 ""gote),"" play on a board ruled into a grid of 12 ""ranks"" (rows) and 12 ""files"" (columns), with a total of 144 squares. The squares are undifferentiated by marking or color, unlike a Western chess board. Each player has a set of 46 pieces of 21 different types, and each piece has its name written on"
"ethics of players, accommodations for physically challenged players, and recording of moves using chess notation. Procedures for resolving irregularities that can occur during a game are provided as well. Chess is played on a chessboard, a square board divided into 64 squares (eight-by-eight) of alternating color, which is similar to that used in draughts (checkers) . No matter what the actual colors of the board, the lighter-colored squares are called ""light"" or ""white"", and the darker-colored squares are called ""dark"" or ""black"". Sixteen ""white"" and sixteen ""black"" pieces are placed on the board at the beginning of the game. The"
"and marble boards are available but rarely accepted for games rated by national or international chess federations. In western chess the board has a squared shape, with its side being divided into eight parts, resulting in a total of sixty-four subdivisions. In other variants, the total number of subdivisions may range from nine to one hundred and twelve. Each subdivision of the board is called a square and receives a unique identification to be used in chess notation, which may be descriptive, algebraic, or numeric. In two-dimensional boards, each horizontal rectilinear array of squares is called a ""rank"", each vertical"
"and 25 ""files"" (columns), for a total of 625 squares. The squares are undifferentiated by marking or color. Each player has a set of 177 wedge-shaped pieces of 93 types. In all, the players must remember 99 moves for these pieces. The pieces are of slightly different sizes. From largest to smallest (or roughly most to least powerful) they are: Several of the English names were chosen to correspond to rough equivalents in Western chess, rather than as translations of the Japanese names. Each piece has its name in the form of two kanji written on its face. On the"
"in 2003. In 2014 FIDE extended this to ban all mobile phones from the playing area during chess competitions, under penalty of forfeiture of the game or even expulsion from the tournament. However, the rules also allow for less rigid enforcement in amateur events. The size of the squares of the chessboard should be approximately 1.25 to 1.3 times the diameter of the base of the king, or 50 to 65 mm. Squares of approximately 57 mm ( inches) normally are well-suited for pieces with the kings in the preferred size range. The darker squares are usually brown or green"
"British Square British Square is a solitaire card game which uses two decks of 52 playing cards each. It has an unusual feature of switchback building whereby each foundation is first built up (from ace to king) and then built down (from king to ace). First sixteen cards are dealt on the tableau into four columns of four cards each, turning it into a ""square."" American rule sets, though, puts the formation of the tableau at sixteen piles, four rows of four piles each. Each pile contains a card at the start of the game. The object of the game"
"to aces. British Square British Square is a solitaire card game which uses two decks of 52 playing cards each. It has an unusual feature of switchback building whereby each foundation is first built up (from ace to king) and then built down (from king to ace). First sixteen cards are dealt on the tableau into four columns of four cards each, turning it into a ""square."" American rule sets, though, puts the formation of the tableau at sixteen piles, four rows of four piles each. Each pile contains a card at the start of the game. The object of"
"Sovereign Chess Sovereign Chess is a commercial chess variant designed by Mark Bates and produced by Infinite Pi Games. The game is played on a 16 x 16 board and begins with 112 pieces—a normal complement of white and black pieces (16 each), and 80 other colored pieces (8 each of 10 different colors). The colored pieces are considered “neutral” at the beginning of the game, and can not initially be moved nor captured. The center of the board contains an arrangement of 24 colored squares (2 each in every color, including white and black), which determine control of the"
"Chess Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid. The game is played by millions of people worldwide. Chess is believed to have originated in India sometime before the 7th century. The game was derived from the Indian game chaturanga, which is also the likely ancestor of the Eastern strategy games xiangqi, janggi, and shogi. Chess reached Europe by the 9th century, due to the Umayyad conquest of Hispania. The pieces assumed their current powers in Spain in the late 15th century; the rules were standardized"
"squares, 17 pale red ""double-word"" squares, of which one, the center square (H8), is marked with a star or other symbol; 12 dark blue ""triple-letter"" squares, and 24 pale blue ""double-letter"" squares. In 2008, Hasbro changed the colors of the premium squares to orange for TW, red for DW, blue for DL, and green for TL, but the original premium square color scheme is still preferred for ""Scrabble"" boards used in tournaments. In an English-language set, the game contains 100 tiles, 98 of which are marked with a letter and a point value ranging from 1 to 10. The number"
"used in hexagonal chess, which utilises a hexagonal board with three different colours for its 91 squares. Boards of different sizes have also been used since the 10th century, with one of the first records being Tamerlane chess, with eleven columns by ten rows. The game originated in Persia and its board contains a peculiar element in the form of the addition of a square to the right of the second row of each player, called a citadel, and which served the purpose of being a refuge for the King and in some cases reaching a draw. Due to the"
"Mutilated chessboard problem The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book ""Critical Thinking"" (1946). It was later discussed by Solomon W. Golomb (1954), and by Martin Gardner in his ""Scientific American"" column ""Mathematical Games"". The problem is as follows: Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares? Most considerations of this problem in literature provide solutions ""in the conceptual sense"" without proofs. John McCarthy proposed it as a"
"is black. Martin Gardner featured puzzles based on checkerboards in his November 1962 Mathematical Games column in Scientific American. A square checkerboard with an alternating pattern is used for games including: The following games require an 8×8 board and are sometimes played on a chessboard. Checkerboard A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which draughts (checkers) is played. Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, often black and white. An 8×8 checkerboard is used to play many other games, including chess, whereby"
"""R"" = ""R"". For the traditional chessboard (""n"" = 2), ""R"" = 4 × 3 × 1 = 12 possible arrangements with rotational symmetry. For (4""n"" + 2) × (4""n"" + 2) and (4""n"" + 3) × (4""n"" + 3) boards, the number of solutions is zero. Two cases are possible for each rook: either it stands in the centre or it doesn't stand in the centre. In the second case, this rook is included in the rook quartet that exchanges squares on turning the board at 90°. Therefore, the total number of rooks must be either 4""n"" (when there"
"the other. In most cases, the squares are not actually white and black, but a light color and a contrasting dark color. For example, the squares on plastic boards are often off-white (""buff"") and green, while those on wood boards are often light brown and dark brown. In old chess writings, the sides are often called Red and Black, because those were the two colors of ink then commonly available when hand-drawing or printing chess position diagrams. As Howard Staunton observed, ""In the earlier ages of chess, the board was simply divided into sixty-four squares, without any difference of colour""."
"5 × 5 board, exactly 204 squares of an infinite chess move that are eight knight's moves from the center, exactly 204 strings of length 11 over a three-letter alphabet with no consecutively-repeated substring, and exactly 204 ways of immersing an oriented circle into the oriented plane so that it has four double points. Both 204 and its square are sums of a pair of twin primes: 204 = 101 + 103 and 204 = 41616 = 20807 + 20809. The only smaller numbers with the same property are 12 and 84. 204 (number) 204 (two hundred [and] four) is"
"Chess on a Really Big Board Chess on a Really Big Board is a large chess variant invented by Ralph Betza around 1996. It is played on a 16×16 chessboard with 16 pieces (on the back rank) and 16 pawns (on the second rank) per player. Since such a board can be constructed by pushing together four standard 8×8 boards, Betza also gave this variant the alternative names of Four Board Chess or Chess on Four Boards. Chess on a Really Big Board was created as an outgrowth of Betza's ideas on three-dimensional chess, after he noted that an 8×8×8"
"as a ""split""). The game is played on a rectangular board with 72 plain squares arranged in 8 ranks and 9 files. The 21 pieces are placed in various locations within the nearest three rows to each player's home side (a total of 27 squares). A player can consider the half of the board nearest him to be ""friendly territory"" while the other side's half is the ""enemy territory,"" though this is not an actual requirement of the game. The two middle rows (fourth rank from each player's edge of the board) are initially empty at the start of the"
"19 line grid is simultaneously an 18 × 18 grid of squares, and the starting position needs only 43 each of the black and white stones. The rules describe a highly variable set of pieces, which will often change every turn. In total there are 510 possible sets of a ""footprint""; however, the starting position uses these rules to emulate chess pieces on a 6×6 board: king, queen, bishop, rook and pawn in this order R–B–Q–K–B–R in the last row (black's view) and 6 pawns in the next row. The game objective, to remove the opponent's ""ring"" (described as a"
"is commonly referred to as ""Western chess"", ""international chess"", ""orthodox chess"", ""orthochess"", and ""classic chess"". Reference aids Lists Chess Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid. The game is played by millions of people worldwide. Chess is believed to have originated in India sometime before the 7th century. The game was derived from the Indian game chaturanga, which is also the likely ancestor of the Eastern strategy games xiangqi, janggi, and shogi. Chess reached Europe by the 9th century, due to the Umayyad conquest of"
"8×8 chessboard is 16, queens - 8, rooks - 8, bishops - 14, knights - 32. Solutions for kings and bishops are shown below. To get 8 independent rooks is sufficient to place them on one of main diagonals. A solution for 32 independent knights is to place them all on squares of the same color (e.g. place all 32 knights on dark squares). Another kind of mathematical chess problems is a ""domination problem"" (or ""covering""). This is a special case of the vertex cover problem. In these problems it is requested to find a minimum number of pieces of"
"At one point there were more than half a million players, and more than 130,000 board sets were sold. Gliński's book ""Rules of Hexagonal Chess"" was published in 1973. The game is played on a vertically oriented regular hexagonal board with sides 6 cells long, which has 91 hex cells having three colours (light, dark, and mid-tone), with the middle cell (or ""hex"") usually mid-tone. The usual set of chess pieces is increased by one bishop and one pawn. The board has 11 , marked by letters ""a""–""l"" (letter ""j"" is not used), and 11 numbered (which bend 60° at"
"square is free. Another chess variant on a 4×5 board, ""Microchess"", was invented by Glimne in 1997. Castling is allowed in this variant. There is also variant on a 4×8 board, ""Demi-chess"", which was invented by Peter Krystufek in 1986. Castling is allowed in this variant. A board needs to be five squares wide to contain all kinds of chess pieces on the first row. In 1969, Martin Gardner suggested a chess variant on 5×5 board in which all chess moves, including pawn double-move, en-passant capture as well as castling can be made. Later AISE (""Associazione Italiana Scacchi Eterodossi"", ""Italian"
"numbers to both files and ranks, with rank 1 being the one closest to the player with the white pieces. The file leftmost to the white player (""a"" in algebraic notation and ""QR"" in descriptive notation) is file one and the rightmost to them (""h"" in algebraic notation and ""KR"" in descriptive notation) is file eight. The usage of chessboards with various shapes goes back to the Persian origins of the game in the 10th century, when the book ""Muraj adh-dhahab"" (Board of the Gods) described six different variants of chess, including circular and cylindrical chess. Another exotic format is"
"Chessboard A chessboard is the type of board game used in the game chess, over which the chess pawns (pieces) are laid. It's usually square in shape, with an alternating pattern of two colours between its subdivisions. Traditionally wooden boards are used of naturally derived light and dark brown woods, while plastic and vinyl boards often use Black or Brown for the dark squares and shades such as buff or cream for the light squares. Materials vary widely; while wooden boards are generally used in high-level games; vinyl, plastic, and cardboard are common for regular and common play. Decorative glass"
"two paths with an even number of squares each, both of which are easy to partition into dominoes. Mutilated chessboard problem The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book ""Critical Thinking"" (1946). It was later discussed by Solomon W. Golomb (1954), and by Martin Gardner in his ""Scientific American"" column ""Mathematical Games"". The problem is as follows: Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares? Most considerations of"
"Quatrochess Quatrochess is a chess variant for four players invented by George R. Dekle, Sr. in 1986. The board comprises 14×14 squares minus the four central squares. Each player controls a standard set of sixteen chess pieces, and additionally nine fairy pieces. The game can be played in partnership (two opposing teams of two) or all-versus-all. Quatrochess was included in ""World Game Review"" No. 10 edited by Michael Keller. The illustration shows the starting setup. White moves first and play proceeds clockwise around the board. Teammates sit in opposite corners in partnership games. The squareless center may not be moved"
"represent the squares on a chess board. Each variable denotes the presence or absence of a queen on that square. Consider that, Although one can solve this problem by constructing OBDDs, it is more efficient to use ZDDs. Constructing a ZDD for the 8-Queens problem requires 8 steps from S1 to S8. Each step can be defined as follows: The Knight’s tour problem has a historical significance. The knight’s graph contains n2 vertices to depict the squares of the chessboard. The edges illustrate the legal moves of a knight. The knight can visit each square of the board exactly once."
"a potential problem, not a major drawback, as most machines will have enough instruction cache for this not to be an issue. The first bit may represent the square a1, and the 64th bit the square h8, in which case a 1 bit followed by 63 0 bits indicates a single piece on the a1 square. Though stored as a 64 bit word (bit array), it can be helpful to think of the words as 8 blocks of 8 bits, each representing a rank (row) on the chess board. There are twelve types of pieces, and each type gets its"